Finite Group Databasebeta

← #11864531

Subgroups — #11864531

Order 1152.

1479 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3#10594855C211yesmaximal, characteristic, complemented
4C22×#3718C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591594C214yesmaximal, complemented
7#10591461C214yesmaximal, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#84117—31nomaximal
11#83983—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—24no—
14C3×#1010—24no—
15C2×C3×D3×Q8C2212yes—
16C2×C3×#237—22no—
17C2×C3×#237C2212yes—
18C2×C3×#235—21no—
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6—21no—
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23#64135C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#951—24no—
26C2×C3×#216C2212yes—
27C2×C3×#214C2212yes—
28C2×C3×#208C2211yescharacteristic
29#63961—22no—
30#63873—21no—
31#63863—21no—
32#63856C2214yes—
33C2×#3718—24no—
34C2×#3718C2214yes—
35#63662C2212yes—
36#63659C2212yes—
37#63566C2214yes—
38(C2×D3)⋊(C3⋊C8)C2214yes—
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic
41C2×C3×#137—31no—
42#5825—31no—
43C2×#951D311yescharacteristic, complemented
44#5816—31no—
45C22×#216—31no—
46C22×#216—31no—
47#5239—34no—
48#5234—31no—
49#5233—31no—
50#5233—31no—
51#5233—61no—
52#5228—34no—
53#5225—31no—
54#5186—34no—
55#5173—34no—
56#5129—31no—
57#5120—31no—
58C32×#41—22no—
59C32×#41D414yes—
60C2×C32×Q8C2311yescharacteristic
61C2×C32×D4—21no—
62C2×C32×D4C2311yescharacteristic
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—22no—
66C2×C3×#67D412yes—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—21no—
70C3×D3×Q8—24no—
71C3×D3×Q8—24no—
72C3×#237—216no—
73C3×#237—24no—
74C3×#237—24no—
75C3×#235—28no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12D411yescharacteristic
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3C2312yes—
81C2×C3×Dic6—28no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—21no—
88C2×C3×Dic6D411yescharacteristic
89C2×C3×Dic6D414yes—
90C2×C3×Dic6C2312yes—
91C2×C3×Dic6C2312yes—
92#3757—21no—
93C4⋊(C3⋊Dic3)C2312yes—
94C4×C3⋊Dic3—21no—
95C2×C3⋊(C3⋊C8)—22no—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#216—24no—
98C3×#214—24no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101#3724—24no—
102(C2×D3)⋊Dic3—24no—
103#3718—28no—
104#3011—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41—62no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—32no—
115C22×C3×Q8—31no—
116C22×C3×Q8—31no—
117C22×C3×Q8—61no—
118#1010—24no—
119#1010—24no—
120C2×D3×Q8C2×D312yes—
121C2×#237—22no—
122C2×#237C2×D312yes—
123C2×#235—21no—
124C2×#235C2×D311yescharacteristic
125C22×Dic6—21no—
126C22×Dic6C2×D311yescharacteristic
127C22×Dic6C2×D311yescharacteristic
128C3×#137—64no—
129C2×C3×Q16—32no—
130C2×C3×SD16—32no—
131C2×C3×M16—31no—
132#951—24no—
133#947—61no—
134#946—34no—
135#944—61no—
136#944—61no—
137C2×#216—34no—
138C2×#216—34no—
139C2×#216—64no—
140C2×#216—64no—
141C2×#216C2×D312yes—
142#936—61no—
143#935—62no—
144C2×#214C2×D312yes—
145#929—62no—
146#926—31no—
147#926—31no—
148#926—61no—
149#924—34no—
150C2×#208C2×D311yescharacteristic
151C22×C3⋊C8—31no—
152C22×C3⋊C8—31no—
153C22×C3⋊C8—61no—
154#835—32no—
155#835—32no—
156#835—34no—
157#835—62no—
158#832—32no—
159#832—32no—
160#832—62no—
161#830—34no—
162(C2×D3)⋊C8—34no—
163#816—34no—
164C23×C32—21no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3C2×D412yes—
167C32×Q8—21no—
168C32×Q8C2×D412yes—
169C32×D4—24no—
170C32×D4—21no—
171C32×D4C2×D412yes—
172C2×C32×C4—21no—
173C2×C32×C4—24no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—22no—
179C3×#67—28no—
180C3×#67—24no—
181C2×C3×Dic3—28no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—42no—
186C2×C3×Dic3C2×D412yes—
187C3×D12—22no—
188C3×C4×D3—28no—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×Dic6—28no—
192C3×Dic6—22no—
193C3×Dic6—24no—
194C3×Dic6—22no—
195C3×Dic6—22no—
196C3×Dic6—22no—
197C3×Dic6—42no—
198C3×Dic6C2×D414yes—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—22no—
201C2×2−1+4—31no—
202C2×#137—31no—
203C22×Q16—91no—
204#536—91no—
205#452—94no—
206#451—94no—
207#419—91no—
208#416—91no—
209#408—91no—
210C3×#41—22no—
211C3×#41—22no—
212C3×#41—24no—
213C3×#41—42no—
214C3×#41—68no—
215C3×#41—64no—
216C3×#41—616no—
217C3×#41—64no—
218C3×#41—62no—
219C3×#41—62no—
220C3×#41#6714yes—
221C3×#41#6714yes—
222C2×C3×Q8—21no—
223C2×C3×Q8—31no—
224C2×C3×Q8—34no—
225C2×C3×Q8—32no—
226C2×C3×Q8—32no—
227C2×C3×Q8—62no—
228C2×C3×Q8—68no—
229C2×C3×Q8—64no—
230C2×C3×Q8—64no—
231C2×C3×Q8—61no—
232C2×C3×Q8—62no—
233C2×C3×Q8—61no—
234C2×C3×Q8—62no—
235C2×C3×Q8—62no—
236C2×C3×Q8C22×D311yescharacteristic
237C2×C3×Q8C22×D311yescharacteristic
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—32no—
242C2×C3×D4—31no—
243C2×C3×D4—41no—
244C2×C3×D4—62no—
245C2×C3×D4C22×D311yescharacteristic
246C2×C3×D4C22×D311yescharacteristic
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—32no—
251C22×C3×C4—41no—
252C22×C3×C4—62no—
253C22×C3×C4—62no—
254C22×C3×C4—61no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—22no—
259C2×#67#6712yes—
260C22×Dic3—21no—
261C22×Dic3—22no—
262C22×Dic3—21no—
263D3×Q8—24no—
264D3×Q8—24no—
265#237—216no—
266#237—24no—
267#237—24no—
268#235—28no—
269#235—22no—
270#235—22no—
271C2×D12#6711yescharacteristic
272C2×C4×D3—22no—
273C2×C4×D3C22×D312yes—
274C2×Dic6—28no—
275C2×Dic6—21no—
276C2×Dic6—22no—
277C2×Dic6—22no—
278C2×Dic6—22no—
279C2×Dic6—22no—
280C2×Dic6—21no—
281C2×Dic6#6711yescharacteristic
282C2×Dic6#6714yes—
283C2×Dic6C22×D312yes—
284C2×Dic6C22×D312yes—
285C3×Q16—64no—
286C3×SD16—64no—
287C3×M16—62no—
288C2×C3×C8—32no—
289#217—64no—
290#217—61no—
291#217—61no—
292#217—121no—
293#216—24no—
294#216—68no—
295#216—68no—
296#214—24no—
297(C2×D3)⋊C4—64no—
298C4⋊Dic3—32no—
299C4⋊Dic3—32no—
300C4⋊Dic3—62no—
301Dic3⋊C4—64no—
302Dic3⋊C4—64no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—121no—
306#208—22no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—122no—
313C2×C3⋊C8C22×D312yes—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—42no—
317C22×C32#12012yes—
318C22×C32C22×D411yescharacteristic
319C2×C3×D3—22no—
320C2×C3×D3—24no—
321C32×C4—22no—
322C32×C4#12012yes—
323C32×C4C22×D411yescharacteristic
324C32×C4C22×D411yescharacteristic
325C3⋊Dic3—42no—
326C3×Dic3—22no—
327C3×Dic3—24no—
328C3×Dic3—42no—
3292−1+4—64no—
3302−1+4—64no—
331C2×#41—31no—
332C2×#41—32no—
333C2×#41—61no—
334C2×#41—62no—
335C2×#41D3211yescharacteristic
336C22×Q8—32no—
337C22×Q8—31no—
338C22×Q8—31no—
339C22×Q8—61no—
340#137—64no—
341C2×Q16—32no—
342C2×Q16—94no—
343C2×Q16—184no—
344C2×SD16—32no—
345C2×M16—31no—
346C22×C8—91no—
347C4⋊Q8—181no—
348#124—181no—
349#123—182no—
350C22⋊Q8—94no—
351#117—91no—
352#103—94no—
353#103—92no—
354#102—92no—
355C22⋊C8—94no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—41no—
361C23×C3D3×D411yescharacteristic
362C23×C3C2×#6711yescharacteristic
363C22×D3C2×#6712yes—
364C3×Q8—21no—
365C3×Q8—21no—
366C3×Q8—22no—
367C3×Q8—34no—
368C3×Q8—41no—
369C3×Q8—68no—
370C3×Q8—62no—
371C3×Q8—64no—
372C3×Q8—62no—
373C3×Q8—62no—
374C3×Q8—62no—
375C3×Q8—122no—
376C3×Q8C2×#6712yes—
377C3×Q8C2×#6712yes—
378C3×D4—24no—
379C3×D4—24no—
380C3×D4—21no—
381C3×D4—21no—
382C3×D4—22no—
383C3×D4—41no—
384C3×D4—44no—
385C3×D4—68no—
386C3×D4—64no—
387C3×D4—62no—
388C3×D4C2×#6712yes—
389C3×D4C2×#6712yes—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—21no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—32no—
399C2×C3×C4—44no—
400C2×C3×C4—41no—
401C2×C3×C4—68no—
402C2×C3×C4—68no—
403C2×C3×C4—64no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—122no—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D412yes—
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C2×#6712yes—
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6712yes—
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—28no—
418#67—24no—
419C2×Dic3—28no—
420C2×Dic3—24no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—42no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—122no—
427C2×Dic3C2×#6712yes—
428D12—22no—
429C4×D3—28no—
430C4×D3—22no—
431C4×D3—22no—
432Dic6—28no—
433Dic6—22no—
434Dic6—24no—
435Dic6—22no—
436Dic6—22no—
437Dic6—22no—
438Dic6—42no—
439Dic6C2×#6714yes—
440C3×C8—62no—
441C3⋊C8—22no—
442C3⋊C8—62no—
443C3⋊C8—62no—
444C3⋊C8—122no—
445C2×C32—22no—
446C2×C32—42no—
447C2×C32C2×#12011yescharacteristic
448C2×C32#57812yes—
449C3×D3—42no—
450#41—22no—
451#41—68no—
452#41—64no—
453#41—616no—
454#41—64no—
455#41—62no—
456#41—62no—
457#41#62514yes—
458C2×Q8—31no—
459C2×Q8—32no—
460C2×Q8—32no—
461C2×Q8—34no—
462C2×Q8—62no—
463C2×Q8—68no—
464C2×Q8—64no—
465C2×Q8—64no—
466C2×Q8—62no—
467C2×Q8—61no—
468C2×Q8—61no—
469C2×Q8—62no—
470C2×Q8—62no—
471C2×Q8C2×D3211yescharacteristic
472C2×D4—21no—
473C2×D4—32no—
474C2×D4—31no—
475C2×D4—62no—
476C2×D4C2×D3211yescharacteristic
477C22×C4—21no—
478C22×C4—32no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4C2×D3211yescharacteristic
484Q16—64no—
485Q16—188no—
486SD16—64no—
487M16—62no—
488C2×C8—32no—
489C2×C8—92no—
490C2×C8—182no—
491C4⋊C4—92no—
492C4⋊C4—184no—
493C22⋊C4—184no—
494C22⋊C4—181no—
495C42—181no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—64no—
507C22×C3—62no—
508C22×C3—82no—
509C22×C3#93712yes—
510C22×C3#95312yes—
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C22×#6711yescharacteristic
513C2×D3—24no—
514C2×D3—22no—
515C3×C4—22no—
516C3×C4—22no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—22no—
520C3×C4—42no—
521C3×C4—62no—
522C3×C4—64no—
523C3×C4—122no—
524C3×C4#93712yes—
525C3×C4#95312yes—
526C3×C4C2×D3×D411yescharacteristic
527C3×C4C22×#6711yescharacteristic
528C3×C4C22×#6711yescharacteristic
529C3×C4C22×#6711yescharacteristic
530Dic3—22no—
531Dic3—24no—
532Dic3—42no—
533Dic3—122no—
534Dic3—122no—
535Dic3—242no—
536C32#301111yescharacteristic, complemented, Sylow
537C23—21no—
538C23—32no—
539C23D3×#6711yescharacteristic
540Q8—21no—
541Q8—34no—
542Q8—68no—
543Q8—62no—
544Q8—62no—
545Q8—64no—
546Q8—62no—
547Q8—62no—
548Q8—122no—
549Q8C2×#62512yes—
550D4—24no—
551D4—21no—
552D4—68no—
553D4—64no—
554D4—62no—
555D4C2×#62512yes—
556C2×C4—21no—
557C2×C4—24no—
558C2×C4—32no—
559C2×C4—68no—
560C2×C4—68no—
561C2×C4—62no—
562C2×C4—64no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—122no—
567C2×C4—182no—
568C2×C4C2×#62512yes—
569C2×C4D3×#6712yes—
570C2×C4D3×#6711yescharacteristic
571C2×C4C22×D3211yescharacteristic
572C8—62no—
573C8—182no—
574C2×C3—22no—
575C2×C3—22no—
576C2×C3—22no—
577C2×C3—21no—
578C2×C3—42no—
579C2×C3—42no—
580C2×C3—42no—
581C2×C3—82no—
582C2×C3—122no—
583C2×C3#577912yes—
584C2×C3C2×#93711yescharacteristic
585C2×C3#583812yes—
586C2×C3C2×#95311yescharacteristic
587D3—42no—
588C22—22no—
589C22—22no—
590C22—42no—
591C22—64no—
592C22—62no—
593C22#6397612yes—
594C22C2×D3×#6711yescharacteristic
595C4—22no—
596C4—62no—
597C4—64no—
598C4—122no—
599C4—362no—
600C4#6397612yes—
601C4C22×#62511yescharacteristic
602C4C2×D3×#6711yescharacteristic
603C3—21no—
604C3#8398311yescharacteristic, complemented
605C3#8411711yescharacteristic, complemented
606C2—22no—
607C2—42no—
608C2—122no—
609C2#1059546512yes—
610C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC2×#41D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. #10594855C2semidirect
4. C22×#3718C2semidirect
5. #10592932C2semidirect
6. #10591594C2semidirect
7. #10591461C2semidirect
8. #10591100C2semidirect
9. #10591071C2semidirect
43. C2×#951D3semidirect
536. C32#3011semidirect
604. C3#83983semidirect
605. C3#84117semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#10102
C2×C3×#9512
#105948552
C22×#37182
#105929322
#105915942
#105914612
#105911002
#105910712
#841173
#839833